Whenever I watch other flycasters, I have a habit of analyzing their casting. I mentally deconstruct their strokes to determine which parts are technically sound, and which parts wither under scrutiny. I ponder what suggestions for improvement I'd pass along if asked, and how I might phrase the wording of those suggestions. Many flaws of technique require a wholesale rebuilding of the casting stroke. Others are more easily fixed. Among the latter is off-plane movement of the rod, a common reason why many fishermen struggle to place their fly where they’re aiming.
Moving the rod in a single plane from the start of a cast to its finish (curve casts and reach casts excepted) is a real key to accuracy. Because the fly line always follows the rod tip, restricting the rod to a single plane forces the line to follow in that same plane. The line scribes a perfectly straight path, facilitating accuracy. Anytime our rod veers off-plane, curves and waves appear in the line. Figuring out where to aim a wavy cast so that the fly ends up on target is no mean feat, usually requiring guesswork and a healthy dose of Kentucky windage. Much better to simply keep the rod in one plane. As long as that plane lines up with the target and the distance of the cast is controlled, the fly will land where it's aimed.
When I say to keep the rod in one plane, note that I'm not specifying at what angle to the ground that plane should be. That's for you to choose. Typically, it will be somewhere between straight overhead (90 degrees to the ground) and sidearm (parallel to the ground). Casting straight overhead provides the greatest accuracy (it's my recommended default position), but particular fishing situations often call for something else. The critical thing is that the rod travels in one plane, regardless of the angle that plane is at relative to the ground.
To see how this works in practice, grab the butt section of your rod. Stand next to a wall so that the shoulder of your casting arm just touches the wall. Simulate the casting stroke, keeping the butt section parallel to the wall. This is how it feels to be on-plane (in this case, in the vertical plane). Now step away from the wall and angle the rod 45 degrees to the floor. Simulate the casting stroke again, taking care to keep the rod in the same plane through the entire stroke. Try this exercise at all angles.
Inaccuracy isn't always fatal to success, but it proves fatal often enough. Minimize those times by becoming a more accurate caster. It's not difficult to do, and a good way to start is by keeping your rod on-plane.